8-Aug-15Created by Mr. Lafferty Maths Dept. Simplifying Algebraic Expressions Removing Brackets Algebra Removing Brackets & Simplifying Evaluating Expressions Factorising – The common factor

8-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6cm 2cm 3cm

8-Aug-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.To remember the phrase ‘ like terms.’ ‘ like terms.’ 1.To review tidying up expressions. Algebra Simplifying Algebraic Expressions 2. To be able to simplify simple algebraic expressions by collecting ‘ like terms.’

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms ( NOT 2b ) ( NOT 8m )

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions y2 y 2 Question : Find the area of each of the 3 sections of this shape. What is the total area. 123

8-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch11 (page 46) Algebra Simplifying Algebraic Expressions

8-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6h 2a 100 o 60 o

8-Aug-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the key steps in removing brackets. 1. To explain how to multiply out simply algebraic brackets. Algebra 2. Apply multiplication rules for integers numbers when removing brackets. Removing brackets

3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 8-Aug-15Created by Mr. Removing a Single Bracket

2(y - 1) =2y - 2 Example 3 7(w - 6) =7w - 42 Example 4 8-Aug-15Created by Mr. Removing a Single Bracket

8(x + 3) =8x + 24 Example 5 4(3 -2m) =12 - 8m Example 6 8-Aug-15Created by Mr. Removing a Single Bracket

Example 7 : Write down an expression for the amount indicate below in two difference ways. 3(x + 3)=3x Aug-15Created by Mr. Removing a Single Bracket x+3

Example 8 : Write down an expression for the amount indicate below in two difference ways. 5(y - 2)= 5y Aug-15 Created by Mr. Removing a Single Bracket y-2

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Y Question : Find the area of the rectangle (i) With brackets (ii) Without brackets. Removing brackets

8-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch11 (page 48) Algebra Removing brackets

8-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm (x+2)cm

8-Aug-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. Explain how to remove brackets and simplify. 1. Understand how to remove brackets Algebra Removing Brackets & Simplifying 3. Tidy up after removing brackets. 2. Apply rules integer numbers.

a(b + 5) =ab + 5a Example 1 p(w - 2) =pw - 2p Example 2 8-Aug-15Created by Mr. Removing a Single Bracket

y(y - 1) =y2y2 - y Example 3 7w(w - 3) =7w w Example 4 8-Aug-15Created by Mr. Removing a Single Bracket

a(a 2 + 3b) =a3a3 + 3ab Example 5 y 2 (3y -2c) =3y 3 - 2cy 2 Example 6 8-Aug-15Created by Mr. Removing a Single Bracket

-(x + y) =-x - y Example 7 -5(a - 7) =-5a + 35 Example 8 8-Aug-15Created by Mr. Removing a Single Bracket

7 + 3(4 - y) = Example (8 - y) = Example 10 8-Aug-15Created by Mr. Removing a Single Bracket - 3y = y Tidy Up + 3y Tidy Up = y

A = 10(x – 2) Example 11 8-Aug-15Created by Mr. Removing a Single Bracket Find my Area (x - 2) 10 Find my Area x 12 A = 12x A = L x BA = L x B

Example 12 : Find area of the orange border 8-Aug-15Created by Mr. Removing a Single Bracket (x - 2) 10 x 12 Area =Big Rec – Small Rec = 12x – 10(x - 2) = 12x – 10x + 20 = 2x + 20

4(m - 3) - (m + 2) =4m m - 2 Example 13 Example 14 8-Aug-15Created by Mr. = 3m - 14 Tidy Up 7(y - 1) - 2(y + 4) =7y y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets

3 x 14 – 8 = 34 A = 4(y – 5) Example 15 : Find an expression for the difference in the areas. 8-Aug-15Created by Mr. (y - 5) 47 A = 7(y- 4) (y- 4) Difference = 7(y - 4) - 4(y – 5) = 7y y + 20 = 3y - 8 Calculate difference if y = 14 Removing Two Single Brackets

2 x =28 A = 7(x + 1) Example 16 : Find an expression for the difference in the areas. 8-Aug-15Created by Mr. (x + 1) 79 A = 9(x + 3) x + 3 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Calculate difference if x = 4 Removing Two Single Brackets

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra x 6 Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section. 4 x-3 Removing Brackets & Simplifying

8-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch11 (page 50) Algebra Removing Brackets & Simplifying

8-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm (x+2)cm

8-Aug-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. To show how to evaluate an expression given values for the letters. 1. Be able to substitute numbers for letters in an expression. Algebra 2. Use previous knowledge to evaluate expression. Evaluating Expressions – number for letter

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 BODMAS

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1

8-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch2 (page 51) Algebra Evaluating Expressions – number for letter

8-Aug-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

8-Aug-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. To show how to reverse the process of removing bracket ‘factorising’. 1. Be able to recognise the HCF for set of values. Algebra 2. Understand the term factorising. Factorising – The Common Factor 3. Factorise simple expressions.

8-Aug-15Created by Mr. Factorising Example Factorise 3x Find the HCF for 3x and HCF goes outside the bracket3( ) 3.To see what goes inside the bracket divide each term by HCF 3x ÷ 3 = x15 ÷ 3 = 53( x + 5 ) Check by multiplying out the bracket to get back to where you started S3 Credit

8-Aug-15Created by Mr. Factorising Example 1.Find the HCF for 4x 2 and 6xy2x 2.HCF goes outside the bracket2x( ) 3.To see what goes inside the bracket divide each term by HCF 4x 2 ÷ 2x =2x6xy ÷ 2x = 3y2x( 2x- 3y ) Factorise 4x 2 – 6xy Check by multiplying out the bracket to get back to where you started S3 Credit

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Simply find the HCF for a given set of data and write the data using brackets :- Factorising – The Common Factor HCF ? 6 4

8-Aug-15Created by Mr. Lafferty Maths Dept. Algebra Simply find the HCF for a given set of data and write the data using brackets :- Factorising – The Common Factor HCF ? a 3 x

8-Aug-15Created by Mr. Factorising Factorise the following : (a)3x + 6 (b) 4xy – 2x (c) 6a + 7a 2 (d)y 2 - y 3(x + 2) 2x(2y – 1) a(6 + 7a) y(y – 1) Be careful ! S3 Credit

8-Aug-15Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch11 (page 54) Algebra Factorising – The Common Factor